Abstract
We consider a system of linear pde describing a cold plasma in a toroidal region in three-dimensional space. This system simulates the passage of a laser beam through the TOKAMAK, it consists of 9 equations for the electric field and the velocities of electrons and ions in a given magnetic field. Asymptotic solutions describing high-frequency Gaussian beams are constructed using the theory of Maslov complex germ in a fairly effective form. The solutions of the system are localized in the neighborhood of the beam passing through the toroidal domain (the camera). The equations for a ray take into account the density of particles in the camera and don't ``feel'' the presence of the magnetic field because of the high frequency of the Gaussian beam; the dependence on the magnetic field is contained in the amplitude of the electric field. Before the TOKAMAK camera the amplitude of the Gaussian beam is the same as in free space, but after the camera the amplitude vector rotates under the influence of the magnetic field. The formula for the angle of rotation is given explicitly. An analytical-numerical algorithm based on the asymptotic solutions is used to analyze the parameters of the magnetic field in the TOKAMAK.